<p>In this research, we conduct a comprehensive analysis of the steady, two-dimensional laminar flow of a non-Newtonian Williamson nanofluid confined between two inclined and fixed parallel plates, subjected to a uniform transverse magnetic field. The nanofluid dynamics are modeled using the Wakif-Buongiorno’s model, which effectively incorporates essential nanoparticle transport mechanisms such as Brownian motion and thermophoresis. By employing appropriate dimensionless variables, the governing equations are systematically transformed into their dimensionless forme, facilitating analytical and numerical treatment. The main contributions of this study lie in the theoretically well-detailed mathematical formulation of the problem. To solve the resulting system of nonlinear ordinary differential equations, we utilize the semi-analytical, the Homotopy Perturbation Method (HPM), and we critically examine its applicability and limitations within the context of our problem. Furthermore, we apply the midpoint Richardson extrapolation technique implemented via the Midrich function in MAPLE software to enhance the accuracy of our solutions. The influence of various dimensionless parameters on the temperature and concentration profiles is systematically investigated, and the findings yield important insights with practical implications for engineering applications, especially in fields where magnetohydrodynamic nanofluid flows are of industrial relevance.</p>